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Journal of Physics B Atomic Molecular and Optical Physics

Faraday waves and droplets in quasi-one-dimensional Bose gas mixtures

F. Kh. Abdullaev, A. Gammal, R. Kishor Kumar, Lauro Tomio

Published Aug 13, 2019• 18 citations
Publisher

Abstract

Abstract Faraday waves in mixtures of Bose gases are studied by taking into account quantum fluctuations beyond the Gross–Pitaevskii mean-field formalism with the Lee–Huang–Yang term. For that, a Bose–Einstein condensed binary atomic mixture is assumed trapped in cigar-type geometry, having the inter- and intra-species scattering lengths periodically varying in time. The period of the Faraday patterns is shown to be quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. By studying the influence of the above nonlinear periodic modulations on quantum droplet dynamics, we also show that nonlinear resonances are excited in the oscillation widths of the quantum droplets. Variational predictions confirm numerical simulations for the corresponding formalism.

DOI
10.1088/1361-6455/ab3ade

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Abstract Faraday waves in mixtures of Bose gases are studied by taking into account quantum fluctuations beyond the Gross–Pitaevskii mean-field formalism with the Lee–Huang–Yang term. For that, a Bose–Einstein condensed binary atomic mixture is assumed trapped in cigar-type geometry, having the inter- and intra-species scattering lengths periodically varying in time. The period of the Faraday patterns is shown to be quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. By studying the influence of the above nonlinear periodic modulations on quantum droplet dynamics, we also show that nonlinear resonances are excited in the oscillation widths of the quantum droplets. Variational predictions confirm numerical simulations for the corresponding formalism.
Abstract Faraday waves (FW) are studied in mixtures of Bose gases by taking into account quantum fluctuations beyond the GP mean-field formalism with the Lee-Huang-Yang term, with both inter-and intra-species scattering lengths periodically varying in time. In this case, the effect of periodic modulations on the system is studied, with nonlinear resonances shown to be excited in the oscillation widths of quantum droplets. It was shown that the period of the Faraday patterns is quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. Variational predictions are confirmed by full numerical simulations. We also add an analysis of quantum droplets and quantum fluctuation contributions when considering three-body interactions.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
Abstract We study Faraday and resonant waves in two-component quasi-one-dimensional (cigar-shaped) collisionally inhomogeneous Bose–Einstein condensates subject to periodic modulation of the radial confinement. We show by means of extensive numerical simulations that, as the system exhibits stronger spatially-localised binary collisions (whose scattering length is taken for convenience to be of Gaussian form), the system becomes effectively a linear one. In other words, as the scattering length approaches a delta-function, we observe that the two nonlinear configurations typical for binary cigar-shaped condensates, namely the segregated and the symbiotic one, turn into two overlapping Gaussian wave functions typical for linear systems, and that the instability onset times of the Faraday and resonant waves become longer. Moreover, our numerical simulations show that the spatial period of the excited waves (either resonant or Faraday ones) decreases as the inhomogeneity becomes stronger. Our results also demonstrate that the topology of the ground state impacts the dynamics of the ensuing density waves, and that the instability onset times of Faraday and resonant waves, for a given level of inhomogeneity in the two-body interactions, depend on whether the initial configuration is segregated or symbiotic.
Abstract We consider Bose–Einstein condensates with two- and three-body interactions periodically varying in time. Two models of time-dependent three-body interactions, with quadratic and quartic dependence on the two-body atomic scattering length a s , are studied. It is shown that parametric instabilities in the condensate lead to the generation of Faraday waves (FWs), with wavelengths depending on the background scattering length, as well as on the frequency and amplitude of the modulations of a s . From an experimental perspective, this opens a new possibility to tune the period of Faraday patterns by varying not only the frequency of modulations and background scattering length, but also the amplitude of the modulations. The latter effect can be used to estimate the parameters of three-body interactions from the FW experimental results. Theoretical predictions are confirmed by numerical simulations of the corresponding extended Gross–Pitaevskii equation.
Abstract In this work, we investigate the modulational instability of plane wave solutions within a modified Gross–Pitaevskii equation framework. The equation features cubic and quartic nonlinearity. It models the behaviour of quasi-one-dimensional Bose–Einstein condensates in symmetric Bose-Bose mixtures of ultra-dilute cold atoms. The cases of equal amplitudes in both species, as well as of unequal amplitudes are studied. Our study demonstrates the pivotal role of the competition between mean-field attractions and quantum fluctuation-induced repulsions. This competition significantly affects the emergence and evolution of modulational instability. By employing linear stability analysis, we identify the essential conditions that lead to modulational instability. We find that the stability of plane wave solutions significantly depends on the interaction among system parameters. Further development of the instability leads to the fragmentation of the BEC into a chain of quantum droplets. We calculated the number of quantum droplets generated during the nonlinear stage of the instability. Our analytical results are corroborated by numerical simulations of the modified quasi-1D Gross–Pitaevskii equation. These simulations vividly depict the formation, interaction, and coalescence of droplets during the nonlinear phase of modulational instability. The investigation shows that the linear stability analysis of the modified Gross–Pitaevskii equation, considering quantum fluctuations, precisely predicts the initial stage of modulational instability phenomena across different domains of parameter space. In contrast, the later nonlinear stage, studied through numerical simulations, reveals the formation and nonintegrable dynamics of quantum droplets.